How did British aircraft fare against Japanese aircraft during the Second World War?

Question:
It goes without saying that both the Supermarine Spitfire used by the UK and the Japanese Mitsubishi Zero are iconic fighter aircraft of the Second World War. But how did these aircraft fare when they were flown against each other (ignoring pilot skill and training)?

Short Answer:
Not many spitfires made it to the Pacific, those that did didn't fair well head to head against the Zero. Some attribute this to tactics employed rather than shortcomings of the aircraft. One legendary commander with an exceptional record against the Zero, made this observation as his squadrons used a lesser plane to great effect against the Zero.

Detailed Answer
The Spitfire and the Zero were both capable planes. A big difference / advantage Zero was tactics. There were relatively few Spitfires allocated to the Pacific theater because Britain kept it's top fighters home. Europe was Britain's priority. Tactics employed successfully against the Germans and Italians in Europe didn't translate well to the Pacific theater of the war.

The Spitfires which did see service in Australia didn't fair well against the zero. Over port town of Darwin the Spitfire's took heavy losses. Notable observer (General Claire Chennault) chalked this up to tactics rather than a short coming of the plane.

Raid on Darwin (May 2, 1943)

                      Strength
        Japanese                Australians and British
        27 Zeros                33 spitfires
        25 Bombers
                      Aircraft lost
        6-10                    14 

That was just one raid.. For almost two years beginning Feb 1942 the airspace over North West Australia was routinely penetrated by Japanese raids, about 70 in total.

Claire Chennault's mercenary pilots, the fying tigers used a slower less capable P40b plane than the spitfire with great effect destroying 296 enemy aircraft, while losing only 14 pilots in combat.

Spitfire was more than 100 mph faster than the zero and the P40b which the Flying Tigers used. The Spitfire had a higher altitude ceiling, more fire power and could out dive the Zero. The Spitfire sacrificed maneuverability and range to the Zero. The Spitfire had about half the range, 1000 miles verse nearly 2000. The Spitfire also could not sustain a steep climb as well as the Zero.
Spitfire vs Zero Stats

Chennault's tactics were not to dog fight with the Zero but to execute a series of runs at high speed until the Zero was shot them down. Chennault discouraged traditional dog fighting against the maneuverable Zero. If you tried to turn with the Zero's the Zero would have the advantage. Chennault's tacts would have been even more effective if employed by a superior plane like the spitfire.

Spitfire's were never deployed to the Pacific in the numbers that facilitated adapting their tactics, but given the P-40B's success against the Zero, we can image what if.

Super Marine Spitfire
The Spitfire also served in the Pacific Theatre, meeting its match in the Japanese Mitsubishi A6M Zero. Lt. Gen. Claire Chennault noted: "The RAF pilots were trained in methods that were excellent against German and Italian equipment, but suicide against the acrobatic Japs." Although not as fast as the Spitfire, the Zero could out-turn the Spitfire with ease, could sustain a climb at a very steep angle, and could stay in the air for three times as long. To counter the Zero, Spitfire pilots had to adopt a "slash and run" policy and use their faster speed and diving superiority to fight, while avoiding classic dogfights.

That Southeast Asia was a lower-priority area also did not help, and it was allocated few Spitfires and other modern fighters compared to Europe, which allowed the Japanese to easily achieve air superiority by 1942. Over the Northern Territory of Australia, Royal Australian Air Force and RAF Spitfires assigned to No. 1 Wing RAAF helped defend the port town of Darwin against air attack by the Japanese Naval Air Force, suffering heavy losses largely due to the type's limited fuel capacity. Spitfire MKVIIIs took part in the last battle of World War II involving the Western allies in Burma, in the ground attack role, helping defeat a Japanese break-out attempt.